Real World Applications – Algebra I

Topic

How much energy could solar panels save for homeowners?

Student Exploration

For this activity, you will need a graphing calculator.

Hook: Watch this video:

Below is a table representing the annual savings on the electricity bill for a homeowner in Los Angeles, CA with a 5.5-kilowatt photovoltaic solar panel system. This system offsets 95% of the homeowner’s electricity use. With electricity rates increasing a certain percentage every year, the homeowner’s savings increased as well.

Year

Annual Savings

2010

$1,175.35

2011

$1,245.87

2012

$1,320.62

2013

$1,399.86

2014

$1,483.85

2015

$1,572.88

2016

$1,667.26

2017

$1,767.29

2018

$1,873.33

2019

$1,985.73

2020

$2,104.87

2021

$2,231.17

Do you think this data represents a linear, exponential or quadratic relationship? Why?

Plot this table in your graphing calculator and create a scatter plot. What are some observations you can make about the data points?

Determine the exponential regression line that fits this data. Write down the equation, and round to the nearest tenth.

What is the initial value? What do you think this means in relation to this situation?

What is the growth factor for this exponential equation? What do you think this represents in relations to this situation?

Using your graph, what do you think the homeowner’s savings will be in 2030? Why? How did you find your answer? Does it make sense?